Math Tutor - Differential Equations Volume 2

“Solving higher order differential equations is challenging for most students simply because the solution methods usually run several pages in length even for the easier problems. The student must identify the type of equation to solve and apply the appropriate solution method, which can lead to valuable lost time on an exam if the wrong solution method is chosen at the outset.We begin by showing the student real life applications of second order and higher ODEs to provide motivation for the material. Next, we show how to solve elemenary second order ODEs, and show the student that all solutions have a similar form.Next, we discuss linear independence of solutions and show the students how to use the wronskian test to determine of a set of functions describe the entire solution space of the ODE.We then get into the core solution techniques which revolve around constant coefficient differential equations. We examine the case where the roots of the characteristic polynomial are real and complex separately, to give the student a good grounding in what to do in either case.Next, we work several problems using the method of undetermined coefficients which allow us to solve higher order ODEs that are more complex. Every step is shown in the solution, and emphasis is placed on showing the student how to properly find the Annihilator function for the right hand side of the equation in the solution.Finally, we use the method of Variation of Parameters to solve several equations and give the student practice in working these problems step by step.Disk 1Sect 1: Intro to Higher Order Differential Equations (ODEs)Sect 2: Identifying Linear ODEsSect 3: Solving Elementary Higher Order ODEsSect 4: The Linear Differential OperatorSect 5: The Wronskian Test For Linearly Independent SolutionsSect 6: Wronskian ProblemsDisk 2Sect 7: Homogeneous ODEs - Constant Coefficients & Real Roots – Part 1Sect 8: Part 2 of AboveSect 9: Part 3 of AboveSect 10: Homogeneous ODEs - Constant Coefficients & Complex Roots – Part 1Sect 11: Part 2 of AboveSect 12: Part 3 of AboveSect 13: Non-Homogeneous ODEs – Undetermined Coefficients – Part 1Sect 14: Part 2 of AboveSect 15: Part 3 of AboveDisk 3Sect 16: Part 4 of AboveSect 17: Part 5 of AboveSect 18: Part 6 of AboveSect 19: Non-Homogeneous ODEs – Variation of Parameters – Part 1Sect 20: Part 2 of AboveSect 21: Part 3 of AboveSect 22: Part 4 of Above”

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